Xandra had some blue and brown marbles. If she gives away 24 blue marbles, the number of blue marbles will be 10% of the total number of marbles left. If she gives away 18 brown marbles, the number of blue marbles will be 25% of the total number of marbles left.

1. How many marbles does Xandra have altogether?
2. What fraction of Xandra's marbles is brown?

	Scenario 1		Scenario 2
	Blue	Brown	Blue	Brown
Before	1 u + 24	9 u	1 p	3 p + 18
Change	- 24	No change	No change	- 18
After	1 u	9 u	1 p	3 p

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

25% = ²⁵₁₀₀ = ¹₄

1 u + 24 = 1 p --- (1)

9 u = 3 p + 18
9 u - 18 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 72 = 3 p --- (3) 

(2) = (3)
9 u - 18 = 3 u + 72 
9 u - 3 u = 72 + 18
6 u = 90

1 u = 90 ÷ 6 = 15

Number of marbles that Xandra had at first
= 1 u + 24 + 9 u
= 10 u + 24
= 10 x 15 + 24
= 150 + 24
= 174

(b)
Number of brown marbles
= 9 u
= 9 x 15
= 135

Fraction of Xandra's marbles that is brown 
= ¹³⁵₁₇₄
= ⁴⁵₅₈

Answer(s): (a) 174; (b) ⁴⁵₅₈